Let $C(u,v)$ be a 2-copula and $W(u,v)=\max(u+v-1,0)$. I want to glue $C$ with $W$ along the curve $u^2+v^2=1$ s.t $$D(u,v)=\begin{cases}u+v-1,& u^2+v^2\ge 1,\\ C(u,v), &u^2+v^2<1 \end{cases}$$
is a copula. Does anyone know references which deal with Copula gluing along some curve $\theta_1(u)+\theta_2(v)=1$ (s.t $\theta_1(u)+\theta_2(v)\le u+v$). Any help is appreciated.